Pinky St. Kira Kira Music Hour/Pinky St. Kira Kira Pop Princess and Pinky St. Kira Kira Music Night/Pop Town are two games I spend a lot of time customising my character on. Whilst you are limited on colours, there are recolours of certain items and each item has a 1, 2, 3 colour choice. (Apart from the faces.) Once you beat the game, you can even change your voice and face. However, unlike the clothes, most hair styles have brown, light brown and dark blue only. But there are many styles.
Even with all this, I guarantee no two custom characters will be the same. (Unless you make them the same, of course.)